Authors:
Darko Dimitrov
;
Christian Knauer
and
Klaus Kriegel
Affiliation:
Freie Universität Berlin, Institute of Computer Science, Germany
Keyword(s):
Computational Geometry, Pattern Matching, 3D Image Registration.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Biomedical Engineering
;
Biomedical Signal Processing
;
Computational Geometry
;
Computer Vision, Visualization and Computer Graphics
;
Data Manipulation
;
Health Engineering and Technology Applications
;
Human-Computer Interaction
;
Image and Video Analysis
;
Image Formation and Preprocessing
;
Image Registration
;
Methodologies and Methods
;
Neurocomputing
;
Neurotechnology, Electronics and Informatics
;
Pattern Recognition
;
Physiological Computing Systems
;
Sensor Networks
;
Soft Computing
;
Surface Geometry and Shape
Abstract:
We study approximation algorithms for a matching problem that is motivated by medical applications. Given a small set of points P ⊂ R3 and a surface S, the optimal matching of P with S is represented by a rigid transformation which maps P as ‘close as possible’ to S. Previous solutions either require polynomial runtime of high degree or they make use of heuristic techniques which could be trapped in some local minimum. We propose a modification of the problem setting by introducing small subsets of so called characteristic points Pc ⊆ P and Sc ⊆ S, and assuming that points from Pc must be matched with points from Sc. We focus our attention on the first nontrivial case that occurs if |Pc | = 2, and show that this restriction results in new fast and reliable algorithms for the matching problem. In contrast to heuristic approaches our algorithm provides guarantees on the approximation factor of the matching. Experimental results are provided for surfaces reconstructed from real and synt
hetic data.
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